This supplement was written for students who are especially good in mathematics and who have a lively interest in the subject. It is suggested that the supplement be read with pencil and paper in hand. All questions should be considered and answered, if possible, when they occur. A casual reading of the supplement is, in most cases, unprofitable. For the most part, the units are independent of each other. Some of the sections in this publication relate to the chapters of the eleventh-grade material of SMSG Intermediate Mathematics. Included in this supplement are suggestions for use of the materials and eight chapters on arithmetic functions, the Euclidean algorithm and linear diophantine equations, the Gaussian integers, Fermat's Method of Infinite Descent, and approximation of irrationals by rationals. (RH)